PHYSICAL REVIEWER 8 VOLUME 39, NUMBER 4

EuzCuo4. An anisotropic Van Vleck paramagnetI

M.- Tovar, * D. Rao, J. Barnett, and S. B.Gsero8'San Diego State University, San Diego, California 92I82

1 FEBRUARY 1989

J. D. Thompson, S-W. Cheong, and Z. FiskLos Alamos National Laboratory, Los Alamos, New Mexico 87545

D. C. Vier and S. SchultzUniversity of California, San Diego, California 92093

(Received 27 June 1988)

Magnetic susceptibility measurements have shown anisotropic Van Vleck paramagnetism in

Eu~Cu04 single crystals. This behavior is associated with the singlet ground state ( Fo) of Eu'+ions, and the measured anisotropy is related to a crystal-field splitting of the excited multiplets ( F&).From the experimental data at low temperatures (T ~ 50 K) a crystal-field parameterA2(r ) = —93(5) cm ' and a spin-orbit coupling constant /=303(15) cm ' have been estimated.The temperature dependence of the magnetic susceptibility is predicted in terms of the Boltzmannpopulation of the excited multiplets, and a comparison with experimental data up to 350 K is made.The possibility of a magnetic contribution arising from the Cu ions is discussed in connection withsome discrepancies observed between the experimental and calculated magnetic susceptibilities.

The discovery of high-T, superconductivity in a seriesof copper oxides, e.g. , (LaSr)zCu04, YBazCu307,Bi2(Ca, Sr)3Cuz09, TlzCazCu30, o, etc. ,

' has led to alarge amount of experimental and theoretical work inthese and other related compounds. All these materialscommonly share layered structures with almost squareplanar Cu-0 arrangement. Some of them are, as men-tioned, high-T, superconductors, while other relatedcompounds have been found to order antiferromagneti-cally, ' such as LazCuO& and YBa2Cu306. Anotherseries of compounds, the (R)2Cu04 family with R=Pr,Nd, Sm, Eu, Gd, form also in a layered tetragonal struc-ture related to the orthorhombic structure of La2Cu04but with a somewhat larger lattice spacing in the planes.These materials are not superconducting or even metallic,and for this reason it is important to study in detail theirmagnetic properties in order to obtain more experimentalevidence on the interplay of magnetic ordering and super-conductivity in these layered copper oxides.

Single crystals of Eu2Cu04 were grown from a PbO-based Aux. The crystal structure is tetragonal with lat-tice constants a =3.910(1)A and c= 11.925(3) A.

The magnetic susceptibility was determined from themagnetization measured in fields up to 5 T, and the re-sults are shown in Fig. 1. The temperature dependence ofthe magnetic susceptibihty corresponds to a Van Vleckparamagnet, as expected for Eu + ions having a singletground state (4f, Fo). Our results show a dependencesimilar to that previously found in polycrystalline materi-al. At the lowest temperatures only the ground state isthermally populated and the susceptibility becomes tern-perature independent. The magnetic moment observed isinduced by the external magnetic field through the ad-mixture of the excited levels into the ground state. The

magnetic susceptibility for such a case is given by

X„=X„gk 1,k

9-

8-0E

EQ), ~

6 ~

O

OC7 5

7-H~c-

4' 1

100I

200T( K)

'300

FIG. 1. Magnetic susceptibility vs temperature of Eu&Cu04,measured with external magnetic field (0.4 T) parallel and per-pendicular to the c-axis. Continuous lines correspond to thecalculated Van Vleck susceptibility.

where Xz is Avogadro's number, H, is the ZeemanHamiltonian, +o and 4& k are the eigenfunctions of theground state Fo and the first excited multiplet F&, re-spectively, and 6, k are the corresponding energies mea-sured from the ground state. A scheme of the energy lev-els is given in Fig. 2.

In the presence of crystal-field interactions the eigen-functions are not pure Fo states but contain componentsfrom other multiplets, thus affecting the matrix elementsin Eq. (1). Besides, as a result of crystal-field eB'ects, the

39 2661 1989 The American Physical Society

2662 M. TOVAR et al. 39

7Fq

B1, B2E (E&=3g -909 cm-~

g-~y5 V2' 321 cm"g+2g5 V2o 264 cm ~

and

g, =F(J= I,E) e(J—=0),

6,=(E(J=2)) —s(J =0),

where y~~and g~ correspond to the magnetic susceptibility

measured with the applied field paralle1 and perpendicu-lar to the c axis, respectively. The parametery=(4&3/15) V2/52 takes into account the crystal-fieldadmixture of the F2 multiplet into the ground state.A~, and Az are the appropriate energy differences givenby

b,~~

=8(J = 1, A p) —E(J =0'),

7Fp 0 0 cm)

CFfree ion tetragonal

FIG. 2. Energy level scheme for Eu + ions in tetragonal sym-metry. The energy values indicated have been estimated fromthe measured Van Vleck magnetic susceptibility of EuCu04.

(3)

pi=2(2+&3y/2) pii/bi,

energy splitting of the Fi multiplet changes the relativeweight of the terms in Eq. (1), giving rise to an anisotrop-ic Van Vleck susceptibility.

Eu ions occupy sites of tetragonal symmetry (C4, ) inthe Eu2Cu04 lattice, and we have thus considered acrystal-field Hami1tonian with the appropriate symmetry:

S=pii(L+2S) EE+aV2020(L)+. . .

where the ellipsis represents fourth- and sixth-orderterms, Oz(L) is a Stevens operator, V2

—= Az(r ), anda=2/45 is the Stevens multiplicative factor for the Fterm. This Hamiltonian splits the F, triplet into a sing-let (A, ) and a doublet (E). The Fz multiplet is split intothree singlets (A „B„and Bz) and one doublet (E), al-though two of the singlets (8, and 82) are accidentallydegenerate when we limit Eq. (2) to second-order opera-tors. The different levels are shown in Fig. 2. Althoughfourth- and sixth-order operators are symmetry allowed,we have not included them into our calculation because(i) the crystal-field splitting of the F, multiplet is deter-mined in first-order perturbation theory only by thesecond-order term of Eq (2); and (ii) even though theneglected higher order terms contribute to the splitting ofthe F2 levels, we are only interested in their admixtureinto the ground state and this can be well approximatedby using the average energy separation that results fromthe spin-orbit interaction. In such a case the expressionsfor the low-temperature limit of the susceptibility reduceto

g (2J +1)(aJ+CJ/kii T) exp[ E(J)/kii T)—J

g (2J + 1) exp[ —8(J)/k~ T](4)

where eJ and CJ are the Van Vleck and Curie constantsfor each multiplet Fz. For the free ions a0=8X„pi, /gand a& = —ao/48. The Curie constants are given by

Cq =gqpli J(J+ 1)/3kii,

where gJ =3/2 for all the excited multiplets. When thereis a crystal-field interaction present, proper eigenvaluesand eigenfunctions should be used to evaluate oJ and CJ.Crystal-field eA'ects for cxo have already been consideredin Eq. (3). The values of CJ, when corrected for the pres-

where ( e(J =2) ) is the average energy of the F2 level.In order to separate the contribution of Eu ions to the

magnetic susceptibility, it is necessary to introducecorrections for core diamagnetism and for the contribu-tion arising from the Cu-0 planes. Since we do not knowwhat the magnetic behavior of the Cu planes is in thismaterial, we have used as total a correction,go=0.06X 10 emu/mol Eu, equal to the measured sus-ceptibility' for LazCu04, averaged over the temperaturerange of our measurements. From the measured valuesat low temperatures, y~~=8. 6(4) X 10 emu/mol Eu and

pi =6.3(3 ) X 10 emu/mol Eu, we have determinedVz = —93(5) cm ' and (=303(15)cm

The value obtained for the crystal-field parameter canbe compared with the predictions of a simple pointcharge model. Gd + ions are surrounded by a distortedcube of oxygen ions whose contribution to the crystalfield is estimated to be A z(r ) =+43 cm ', assuming ashielding factor" (1 —o z) =0.20. The order of magnitudeis correct, but the opposite sign is obtained. Only minorchanges are observed if semiempirical parameters" areconsidered for the Eu +-O interaction. This result is notunexpected, since second-order crystal-field parametersusually have significant contributions from distant ionsand also from dipolar or quadrupolar polarization of theions of the lattice. In fact, we have observed that includ-ing neighbors up to a distance of S A reverses the sign ofthe calculated parameter.

At higher temperatures the excited levels becomethermally populated and, in the absence of a crystal field,the susceptibility is given by Van Vleck's formula

39 Eu2Cu04. AN ANISOTROPIC VAN VLECK PARAMAGNET 2663

ence of crystal-field effects, result in the following expres-sions:

C", =C,(1+,V', Zk, T)

and

C, =C, ( 1 ——,' V2 Iktt T)

for the first excited multiplet, and similar expressions canbe derived for the other excited levels. The Boltzmannfactors should also be modified to include the splitting-ofthe multiplets.

The results of this calculation are shown in Fig. 2 as acontinuous line. It should be mentioned that this esti-mate does not significantly depend on the neglectedfourth- and sixth-order terms in Eq. (2)

The differences between the experimental and calculat-ed values are of the order of 2X10 " emu/mol Eu atroom temperature, and are beyond both the experimentalresolution and the estimated uncertainties of the calculat-ed curves. The temperature dependence of the magneticsusceptibility is dominated by the energy differences be-tween the ground state and the excited states of the Euions. Unfortunately, there are no optical data availableto check our estimates for these energies, derived underthe assumption that the contribution from Cu planes areas small as in the metallic compound La2Cu04. Howev-er, it is interesting to notice that the value estimated forthe spin-orbit parameter /=303 cm ' is smaller than thevalues observed in other compounds, ' i.e., the measuredaverage low-temperature susceptibility is larger in thismaterial. This fact makes likely the existence of largermagnetic contributions from Cu planes for Eu2CuQ4.For example, if we arbitrarily assume that their contribu-tion is temperature independent, isotropic, and equivalent

to 3 X 10 emu/mol Eu, and subtract it from the mea-sured susceptibilities, then the estimated spin-orbit valuewould be /=315 cm ' and the crystal-field parameterVz=- —100 cm '. These values imply energies for thefirst excited levels of 275 cm ' and 335 cm ', respective-ly. These values are larger than those previously derivedand could result in a smaller decrease of the susceptibili-ties with temperature. In particular these values wouldmake a better fit of the data.

In conclusion, we have found that Eu2CuO4 is a VanVleck paramagnet whose magnetic anisotropy can be re-lated to the crystal-field splitting of the excited multi-plets. We have also found indications that the Cu-Oplanes have a non-negligible contribution to the measuredmagnetic susceptibility. If that is indeed the case, somekind of magnetic order must be present because nosignificant paramagnetic Curie-like behavior is observedat low temperatures. This observation is consistent withthe Mossbauer results' which indicate correlated spinbehavior up to temperatures above 400 K, and also withelectron spin resonance experiments' that show anantiferromagnetic-like low field resonance line below-200 K. The existence of magnetic ordering at thesetemperatures is not unexpected since the same order ofmagnitude coupling is seen here' between Cu spins as inLazCu04 which orders antiferromagnetically at 220 K.

ACKNOWLEDGMENTS

We wish to acknowledge partial support from theComision Nacional de Energia Atomica (Argentina),from the National Science Foundation under ContractNo. NSF-DMR 86-13856, and from the United StatesDepartment of Energy (the work done at Los AlamosNational Laboratory).

Permanent address: Centro Atomico Bariloche, 8400 Bari-loche, Rio Negro, Argentina.

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